Complex Analysis of Ground Deformation and Stress for a Shallow Circular Tunnel with a Cavern in the Strata considering the Gravity Condition

In the urban strata, the caverns appear inevitably due to the leakage of pipelines, the constructions of underground structures and other factors. For shallow tunnels, the influences of caverns on the ground deformation and stress during the tunneling construction cannot be ignored, which may endangers the surrounding understructures and nearby superstructures. Therefore, the interaction between the tunnel and the cavern should be considered seriously. In order to achieve ground deformation and stress for a shallow circular tunnel with a cavern in the strata, an analytical model that can take into account the gravity and the interaction between the tunnel and the cavern is proposed in this paper. In the model, the initial gravity condition is considered on the tunnel boundary, and the stress free condition is taken into account on the cavern boundary. During the solving process, the complex variable method and the Schwarz alternating method are applied. Then the analytical solution is verified by a corresponding numerical model. The results show that the analytical solution for the deformation and stress on the tunnel boundary agrees very well with the numerical solution. Finally, the influences of the cavern on the hoop stresses, radial deformations along the tunnel boundary and the surface settlements are discussed based on the solution proposed. The research shows important theoretical significances and application potentials for the prediction of the ground stress and deformation caused by the shallow tunnel with a cavity in the stratum.